The alpha power Weibull distribution is a flexible generalization of the classical Weibull distribution that is capable of modeling a wide variety of data behaviors through its ability to accommodate multiple shapes of the hazard rate function. This flexibility makes it an attractive model for reliability and lifetime data analysis. Motivated by practical data collection constraints, this study investigates statistical inference for the alpha power Weibull distribution under the adaptive progressive Type-II censoring scheme. Classical estimation based on the maximum likelihood method is considered alongside Bayesian inference. In addition to the commonly used Metropolis-Hastings algorithm, this paper explores, for the first time, Bayesian estimation of the model parameters and associated reliability measures using the Hamiltonian Monte Carlo algorithm. Both point estimation and interval estimation are addressed, including asymptotic confidence intervals within the classical framework and highest posterior density credible intervals under the Bayesian approaches. The proposed methods are examined through a simulation study and an application to real data. The numerical results indicate that the Hamiltonian Monte Carlo algorithm provides more stable and efficient Bayesian inference under the adaptive progressive Type-II censoring plan when compared with the Metropolis-Hastings algorithm.
Nassar et al. (Fri,) studied this question.